Quantum computational logic with mixed states

TL;DR

This paper develops an algebraic framework for quantum computational logic with mixed states, proving axiomatizability and establishing a strong completeness theorem for the logic.

Contribution

It introduces a Hilbert-style calculus for quantum logic with mixed states and proves its algebraic strong completeness, addressing a previously open problem.

Findings

Established axiomatizability of quantum computational logic with mixed states

Developed a Hilbert-style calculus for the logic

Proved an algebraic strong completeness theorem

Abstract

Using an algebraic framework we solve a problem posed in [5] and [7] about the axiomatizability of a quantum computational type logic related to fuzzy logic. A Hilbert-style calculus is developed obtaining an algebraic strong completeness theorem.